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Numbers k such that k^2 has k as its middle digits.
4

%I #14 Jul 17 2021 04:30:13

%S 1,50,60,250,3792,7600,376000,495475,625000,971582,66952741,93760000,

%T 177656344,3199268655,9062500000,10937600000,788138178328,

%U 860628177919,890625000000,2291665833333,2780225311054,2890625000000,71093760000000,128906250000000

%N Numbers k such that k^2 has k as its middle digits.

%C Some of the terms are automorphic numbers (A003226) multiplied by an appropriate power of 10. a(25) > 10^15. - _Giovanni Resta_, Jul 29 2013

%D Computed by _Robert Israel_.

%e a(5)=3792 because 3792^2 = 14379264 has 3792 as its middle digits.

%t Do[ If[ StringPosition[ ToString[n^2], ToString[n]] [[1, 1]] == (Ceiling[ Log[10, n^2] ] - Ceiling[ Log[10, n] ])/2 + 1, Print[n] ], {n, 1, 10^9} ]

%Y k^2 is given in A062120.

%K nonn,base,nice

%O 1,2

%A Brian Wallace (wallacebrianedward(AT)yahoo.co.uk), Jun 28 2001

%E Corrected and extended by _Robert G. Wilson v_, Aug 08 2001

%E a(15)-a(24) from _Giovanni Resta_, Jul 29 2013